I agree with you that peace won't drop out of the sky (collective.) Wars and such seem to be the fruits of the collective/herd mentality. Trying to join all the collectives together will likely lead to sudden fragmentation, as can be witnessed via family strife, civil unrest, etc, within the tribal collectives we see today. One might even point to the joining together of the people "with one mind" at the biblical story of the tower of Babel, followed by the sudden fragmentation of this "super collective." I would say that looking to a different place would probably be more prudent, as the collective egregores are susceptible to poisoning by greed, hatred, or delusion from the individual minds of the collective, and that poison then quickly spreads to other individuals in that collective. I would say a more effective place to concentrate efforts for change would be for each individual to look within themselves, resolve any poisons like greed, hatred, or delusion they find there, and make themselves resistant to these poisons that might be spreading among any collective they might be influenced by.
I also agree with you that education is important. Individuals need to be able to think for themselves in order to resist poisons spread via collective egregores. I just disagree that a single supercollective will solve the problem. (As you said, "Peace won't drop out of the sky.") Individuals have to look within and cure themselves first.